From the ABRSM G5 workbook.
To my mind the excerpt could be in F minor or B flat minor, both contain flat BED (and A). The answer given is B flat minor; why is it not F minor?
(Saw this after posting: is the A natural, sharp 7th that trends it to B flat?)
I guess it's because of this workbook, but you've posted a couple of other similar questions. It's not your fault, but these exam questions have a lot of difficulties or dangers. We should never assume that a passage "may" only use the notes of a certain scale, so therefore the notes it uses aren't an ironclad guarantee of the key. That means that you can never show someone an handful of notes and say "With 100% certainty, what key is this?" These questions are asking you, then, to do "best-guess" answers, to use "Occam's razor" to guess the simplest and most likely scenario.
They're asking you not just to look at this as a melody, but to deduce likely harmonic chords, and from those the likely tonality. For instance, the simplest case for this one would be Bbm for two beats, Ebm for two, then F for the last bar. Although this makes the excerpt end on an F chord, it sets up a half cadence: i, iv, V.
It would be unlikely for the excerpt to be in F minor since that has an A flat. While you could find ways to work an A natural into an F minor excerpt, it's hard to imagine those ways fitting this sequence of notes.
